A G‐KKM type theorem and its applications to minimax inequalities on G‐convex spaces

A G‐KKM type theorem is obtained on G‐convex spaces. As application, a generalization of Ky Fan′s minimax inequality to non‐compact sets on G‐convex spaces is first obtained. As special cases of this minimax inequality, some new minimax inequalites are obtained. Four fixed point theorems and four equivalent formulations of the second minimax inequality are also obtained.